One problem with legislation - especially when it comes to vehicles - is how it changes constantly.
Another is how what goes in one state (or territory) may not go in another. (Case in point: transferring the 780's rego from NSW to TAS).
A really big problem is what they passed yesterday, they may not pass today.
Relevant QLD guides are here - these are 'living documents' so they should be up to date -
https://www.tmr.qld.gov.au/Safety/Vehicle-standards-and-modifications/Vehicle-modifications/Light-vehicle-modifications
And here:
https://www.tmr.qld.gov.au/Safety/Vehicle-standards-and-modifications/Vehicle-standards/Vehicle-standards-instructions
This relates to smog testing:
https://www.tmr.qld.gov.au/-/media/Safety/Vehicle-standards-and-modifications/Vehicle-standards/Vehicle-standards-instructions/L203.pdf?la=en
Then, of course, there's VSB 14:
https://www.tmr.qld.gov.au/-/media/Safety/Vehicle-standards-and-modifications/Vehicle-modifications/Light-vehicle-modifications/NCOP/4sectionlaengine.pdf?la=en
Having semi-digested all of that, and also what's been written so far here, my thoughts (rightly or wrongly) are as follows:
The R-Sport turbo kit was developed for the Volvo Turbo Cup cars in Sweden circa 1980-1 IIRC, I don't recall it being sold here as a factory fitted accessory. Factory 240s were equipped with B21 K-Jet turbos, not B23 or B230 turbos with LH or Motronic. A 242GT would be subject to the requirements of at least ADR-27A in terms of what pollution gear it's required to have, unless an ADR-37 compliant engine is fitted. A bog stock B23ET from a 1983 760T (with Motronic version-whatever it had, which wasn't K-Jet) would be ADR-27A compliant. A B230FT with LH2.2 or 2.4 would be ADR-37 compliant, with cats. A turbocharged B23 or B230 fits into the capacity limit for a 240 under section 2.13, Table LA1. QLD doesn't have an IM240 gas emission testing facility, so the requirement for an actual gas test has been waived - see Vehicle Standards Instruction (Light Vehicle 20.3).
Conclusion? Talk to someone at QLD transport - it may be as simple as sticking a nice big high flow fat cat on it, and it's unlikely they'll knock you back.